Mathematical Support of On-board Radio Electronic Device for Aircraft Takeoff Parameters Control

The article provides a physical and mathematical description of the dynamics of an aircraft take-off. It is shown how to establish the correlation between the distance actually covered by the aircraft (related to speed gained during the aircraft take-off) and the safe distance that has to be covered with the same dynamic characteristics up to the end of the runway. A system of differential equations involving the forces acting on the aircraft during its movement is presented. A complete solution of this system is given with the functional time-dependences of the speeds and distances covered by the aircraft. Based on these equations, a formula is derived that allows to assess the situation during takeoff. The algorithm implemented into the corresponding electronic device is assumed to permit the crew to decide whether to continue taking-off in a regular mode or to interrupt it and start braking in order to avoid the emergency of the aircraft rollout outside the runway.